%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET909+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:00:40 PM UTC 2025 % Result : Theorem 6.74s 6.97s % Output : Proof 6.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET909+1 : TPTP v9.2.0. Released v3.2.0. % 0.11/0.12 % Command : duper %s % 0.11/0.32 % Computer : n010.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Thu Oct 2 13:54:53 EDT 2025 % 0.11/0.32 % CPUTime : % 6.74/6.97 SZS status Theorem for theBenchmark.p % 6.74/6.97 SZS output start Proof for theBenchmark.p % 6.74/6.97 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), Eq (unordered_pair A B) (unordered_pair B A)) True % 6.74/6.97 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Eq (set_union2 A B) (set_union2 B A)) True % 6.74/6.97 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), Iff (Eq A empty_set) (∀ (B : Iota), Not (in B A))) True % 6.74/6.97 Clause #4 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (unordered_pair A B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D A) (Eq D B)))) True % 6.74/6.97 Clause #5 (by assumption #[]): Eq (∀ (A B C : Iota), Iff (Eq C (set_union2 A B)) (∀ (D : Iota), Iff (in D C) (Or (in D A) (in D B)))) True % 6.74/6.97 Clause #12 (by assumption #[]): Eq (Not (∀ (A B C : Iota), Ne (set_union2 (unordered_pair A B) C) empty_set)) True % 6.74/6.97 Clause #26 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (unordered_pair a B) (unordered_pair B a)) True % 6.74/6.97 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (Eq (unordered_pair a a_1) (unordered_pair a_1 a)) True % 6.74/6.97 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (unordered_pair a a_1) (unordered_pair a_1 a) % 6.74/6.97 Clause #38 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (set_union2 a B) (set_union2 B a)) True % 6.74/6.97 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (Eq (set_union2 a a_1) (set_union2 a_1 a)) True % 6.74/6.97 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Eq (set_union2 a a_1) (set_union2 a_1 a) % 6.74/6.97 Clause #41 (by clausification #[3]): ∀ (a : Iota), Eq (Iff (Eq a empty_set) (∀ (B : Iota), Not (in B a))) True % 6.74/6.97 Clause #43 (by clausification #[41]): ∀ (a : Iota), Or (Eq (Eq a empty_set) False) (Eq (∀ (B : Iota), Not (in B a)) True) % 6.74/6.97 Clause #51 (by clausification #[4]): ∀ (a : Iota), % 6.74/6.97 Eq (∀ (B C : Iota), Iff (Eq C (unordered_pair a B)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D B)))) True % 6.74/6.97 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), % 6.74/6.97 Eq (∀ (C : Iota), Iff (Eq C (unordered_pair a a_1)) (∀ (D : Iota), Iff (in D C) (Or (Eq D a) (Eq D a_1)))) True % 6.74/6.97 Clause #53 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), % 6.74/6.97 Eq (Iff (Eq a (unordered_pair a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2)))) True % 6.74/6.97 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 6.74/6.97 Or (Eq (Eq a (unordered_pair a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) % 6.74/6.97 Clause #64 (by clausification #[43]): ∀ (a : Iota), Or (Eq (∀ (B : Iota), Not (in B a)) True) (Ne a empty_set) % 6.74/6.97 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (Not (in a_1 a)) True) % 6.74/6.97 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Ne a empty_set) (Eq (in a_1 a) False) % 6.74/6.97 Clause #67 (by destructive equality resolution #[66]): ∀ (a : Iota), Eq (in a empty_set) False % 6.74/6.97 Clause #69 (by clausification #[12]): Eq (∀ (A B C : Iota), Ne (set_union2 (unordered_pair A B) C) empty_set) False % 6.74/6.97 Clause #70 (by clausification #[69]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) B) C) empty_set)) True % 6.74/6.97 Clause #71 (by clausification #[70]): ∀ (a : Iota), Eq (∀ (B C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) B) C) empty_set) False % 6.74/6.97 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), Eq (Not (∀ (C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C) empty_set)) True % 6.74/6.97 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) C) empty_set) False % 6.74/6.97 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 6.74/6.97 Eq (Not (Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) empty_set)) True % 6.74/6.97 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 6.74/6.97 Eq (Ne (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) empty_set) False % 6.74/6.97 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (set_union2 (unordered_pair (skS.0 4 a) (skS.0 5 a a_1)) (skS.0 6 a a_1 a_2)) empty_set % 6.74/6.97 Clause #79 (by superposition #[76, 40]): ∀ (a a_1 a_2 : Iota), Eq empty_set (set_union2 (skS.0 6 a a_1 a_2) (unordered_pair (skS.0 4 a) (skS.0 5 a a_1))) % 6.82/7.01 Clause #85 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B C : Iota), Iff (Eq C (set_union2 a B)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D B)))) True % 6.82/7.01 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota), % 6.82/7.01 Eq (∀ (C : Iota), Iff (Eq C (set_union2 a a_1)) (∀ (D : Iota), Iff (in D C) (Or (in D a) (in D a_1)))) True % 6.82/7.01 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota), Eq (Iff (Eq a (set_union2 a_1 a_2)) (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2)))) True % 6.82/7.01 Clause #89 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), % 6.82/7.01 Or (Eq (Eq a (set_union2 a_1 a_2)) False) (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) % 6.82/7.01 Clause #172 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), % 6.82/7.01 Or (Eq (∀ (D : Iota), Iff (in D a) (Or (Eq D a_1) (Eq D a_2))) True) (Ne a (unordered_pair a_1 a_2)) % 6.82/7.01 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Eq (Iff (in a_3 a) (Or (Eq a_3 a_1) (Eq a_3 a_2))) True) % 6.82/7.01 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 a_3 : Iota), % 6.82/7.01 Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (Eq a_3 a_1) (Eq a_3 a_2)) False)) % 6.82/7.01 Clause #176 (by clausification #[174]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Eq a_3 a_2) False)) % 6.82/7.01 Clause #178 (by clausification #[176]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (unordered_pair a_1 a_2)) (Or (Eq (in a_3 a) True) (Ne a_3 a_2)) % 6.82/7.01 Clause #179 (by destructive equality resolution #[178]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (unordered_pair a_1 a_2)) True) (Ne a a_2) % 6.82/7.01 Clause #180 (by destructive equality resolution #[179]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a_1 a)) True % 6.82/7.01 Clause #183 (by superposition #[180, 28]): ∀ (a a_1 : Iota), Eq (in a (unordered_pair a a_1)) True % 6.82/7.01 Clause #265 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Or (Eq (∀ (D : Iota), Iff (in D a) (Or (in D a_1) (in D a_2))) True) (Ne a (set_union2 a_1 a_2)) % 6.82/7.01 Clause #266 (by clausification #[265]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Eq (Iff (in a_3 a) (Or (in a_3 a_1) (in a_3 a_2))) True) % 6.82/7.01 Clause #267 (by clausification #[266]): ∀ (a a_1 a_2 a_3 : Iota), % 6.82/7.01 Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (Or (in a_3 a_1) (in a_3 a_2)) False)) % 6.82/7.01 Clause #269 (by clausification #[267]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (set_union2 a_1 a_2)) (Or (Eq (in a_3 a) True) (Eq (in a_3 a_2) False)) % 6.82/7.01 Clause #271 (by destructive equality resolution #[269]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 a_2)) True) (Eq (in a a_2) False) % 6.82/7.01 Clause #274 (by superposition #[271, 183]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (set_union2 a_1 (unordered_pair a a_2))) True) (Eq False True) % 6.82/7.01 Clause #280 (by clausification #[274]): ∀ (a a_1 a_2 : Iota), Eq (in a (set_union2 a_1 (unordered_pair a a_2))) True % 6.82/7.01 Clause #308 (by superposition #[79, 280]): ∀ (a : Iota), Eq (in (skS.0 4 a) empty_set) True % 6.82/7.01 Clause #326 (by superposition #[308, 67]): Eq True False % 6.82/7.01 Clause #335 (by clausification #[326]): False % 6.82/7.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------